Ratio & Proportion - Free MCQ Test with solutions, Bank Exams NCERT Mathematics

To find the value of x when the numbers 7, 14, x, and 12 are in proportion, we can use the concept of ratios.

In a proportion, the product of the means equals the product of the extremes. This can be expressed as:

• 7 × 12 = 14 × x

Now, we can calculate:

• 7 × 12 = 84
• 14 × x = 84

Next, we can isolate x:

• To find x, divide both sides by 14:
• x = 84 ÷ 14
• x = 6

Thus, the value of x is 6.

To find the value of x in the proportion of 10, x, 15, and 3, we can use the concept of equivalent ratios. The relationship can be expressed as:

• 10 : x = 15 : 3

This means that the ratio of 10 to x is the same as the ratio of 15 to 3. To solve for x, we can cross-multiply:

• 10 * 3 = 15 * x

This simplifies to:

• 30 = 15x

Next, divide both sides by 15 to isolate x:

• x = 30 / 15
• x = 2

Thus, the value of x is 2.

To find the value of x when the numbers 18, 16, 99, and x are in proportion, we can use the concept of proportions.

Proportions state that if a, b, c, and d are in proportion, then:

• a : b = c : d

This can be written as:

• a × d = b × c

In our case:

• a = 18
• b = 16
• c = 99
• d = x

Now, substituting the values into the proportion gives:

• 18 × x = 16 × 99

Calculating the right side:

• 16 × 99 = 1584

Now, we have:

• 18 × x = 1584

To find x, divide both sides by 18:

• x = 1584 / 18

Calculating the division:

• x = 88

Thus, the value of x is 88.

The mean proportion of two numbers, 9 and 16, can be calculated as follows:

• First, identify the two numbers.
• Next, find the geometric mean using the formula: √(a × b), where a and b are the numbers.
• In this case: √(9 × 16) = √144.
• The result is 12.

Thus, the mean proportion of 9 and 16 is 12.

The mean proportion between two numbers is calculated by finding the square root of their product. In this case, we need to find the mean proportion of 4 and 16.

• First, multiply the two numbers: 4 × 16 = 64.
• Next, take the square root of the result: √64 = 8.

Therefore, the mean proportion of 4 and 16 is 8.

The ratio of boys to girls can be calculated by comparing their numbers directly. In this case:

• There are 20 boys in total.
• There are 40 girls in total.

To find the ratio:

• We compare the number of boys to the number of girls, which is 20:40.
• This ratio can be simplified:
• Divide both sides by 20.
• This results in a simplified ratio of 1:2.

Therefore, the final answer is that the ratio of boys to girls is 1:2.

To find the ratio of the length of a room to its breadth, you can follow these steps:

• The length of the room is 30 m.
• The breadth of the room is 20 m.
• The ratio is calculated by dividing the length by the breadth:
• Ratio = Length : Breadth = 30 m : 20 m.

To simplify the ratio:

• Divide both numbers by their greatest common divisor, which is 10.
• Thus, 30 ÷ 10 = 3 and 20 ÷ 10 = 2.

This gives us a simplified ratio of 3:2.

To find the cost of 4 cans of juice, we first need to determine the price per can based on the given information.

• The cost of 6 cans is Rs 210.
• To calculate the cost of one can, divide the total cost by the number of cans:
• Cost per can = Rs 210 ÷ 6 = Rs 35.
• Next, multiply the cost per can by the number of cans you want to find the cost for:
• Cost of 4 cans = Rs 35 × 4 = Rs 140.

Therefore, the cost of 4 cans of juice is Rs 140.

To calculate the distance covered in 3 hours at a constant speed, follow these steps:

• First, determine the speed of the car. The car travels 90 km in 2.5 hours.
• Calculate the speed using the formula: Speed = Distance / Time.
• Thus, the speed is: Speed = 90 km / 2.5 hours = 36 km/h.
• Now, to find the distance covered in 3 hours, use the formula: Distance = Speed × Time.
• So, the distance is: Distance = 36 km/h × 3 hours = 108 km.

The distance covered in 3 hours at the same speed is 108 km.

The number of holidays in a year is 73. To find the ratio of holidays to days in a year, we need to consider the total number of days in a year, which is typically 365.

• To calculate the ratio, we express it as holidays:days.
• This can be written as 73:365.
• Next, we simplify this ratio:
• Divide both numbers by their greatest common divisor (GCD).
• The GCD of 73 and 365 is 1, so the ratio remains 73:365.
• To convert this ratio into a more understandable format, we can express it as:
• 1 holiday for every approximately 5 days (since 365 ÷ 73 ≈ 5).

Hence, the simplified ratio of the number of holidays to the number of days in a year is 1:5.

When two fractions are equal, they are said to be in proportion.

In understanding proportions, consider the following points:

• Fractions represent parts of a whole.
• When fractions are equal, their ratios are the same.
• This equality indicates a relationship of balance.

For example, if you have the fractions 1/2 and 2/4, they are equal:

• 1/2 = 2/4
• Thus, they are in proportion.

Recognising proportions is essential in various fields, such as mathematics, science, and finance, as it helps in comparing quantities effectively.

To find the ratio of females to males in the office, follow these steps:

• Total number of persons: 45
• Number of females: 25
• Number of males: 45 - 25 = 20

Now, we can express the ratio of females to males:

• Ratio: Number of females (25) to number of males (20)
• This can be simplified as:
• 25:20
• Dividing both sides by 5 gives:
• 5:4

Thus, the ratio of females to males is 5:4.

To find the ratio of the number of males to females in the office, follow these steps:

• The total number of persons in the office is 45.
• The number of females is 25.
• To find the number of males, subtract the number of females from the total: 45 - 25 = 20.
• This means there are 20 males.
• The ratio of males to females is calculated as: 20 males : 25 females.
• Simplifying this ratio:
  • Divide both sides by 5: 4 : 5.

The final ratio of males to females is 4:5.

To find the ratio of 81 to 108, follow these steps:

• Start by dividing both numbers by their greatest common divisor (GCD).
• The GCD of 81 and 108 is 27.
• Now, divide both numbers by 27:
• 81 ÷ 27 = 3
• 108 ÷ 27 = 4
• This gives us the simplified ratio of 3:4.

Therefore, the ratio of 81 to 108 is 3:4.

To find the ratio of 30 minutes to 1.5 hours, follow these steps:

• Convert 1.5 hours into minutes:
  • 1 hour = 60 minutes
  • 1.5 hours = 1.5 × 60 = 90 minutes
• Now, compare 30 minutes to 90 minutes.
• The ratio can be expressed as: 30 minutes : 90 minutes.
• To simplify this ratio:
  • Divide both sides by 30:
  • 1 : 3

Thus, the ratio of 30 minutes to 1.5 hours is 1:3.